# Chapter 5. Implementing Risk Forecasts (in MATLAB/Python)

Copyright 2011, 2016, 2018 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: https://www.gnu.org/licenses/.
The original 2011 R code will not fully work on a recent R because there have been some changes to libraries. The latest version of the Matlab code only uses functions from Matlab toolboxes.
The GARCH functionality in the econometric toolbox in Matlab is trying to be too clever, but can't deliver and could well be buggy. If you want to try that, here are the docs (estimate). Besides, it can only do univariate GARCH and so can't be used in Chapter 3. Kevin Sheppard's MFE toolbox is much better, while not as user friendly, it is much better written and is certainly more comprehensive. It can be downloaded here and the documentation here is quite detailed.

##### Listing 5.1/5.2: Download stock prices in MATLAB Last updated August 2016

p1 = stocks(:,1);                   % consider first two stocks
p2 = stocks(:,2);
y1=diff(log(p1));                   % convert prices to returns
y2=diff(log(p2));
y=[y1 y2];
T=length(y1);
value = 1000;                       % portfolio value
p = 0.01;                           % probability

##### Listing 5.1/5.2: Download stock prices in Python Last updated June 2018

import numpy as np
p = p[:,[0,1]]                                        # consider two stocks
## convert prices to returns, and adjust length
y1 = np.diff(np.log(p[:,0]), n=1, axis=0)
y2 = np.diff(np.log(p[:,1]), n=1, axis=0)
y1 = y1[len(y1)-4100:]
y2 = y2[len(y2)-4100:]
y = np.stack([y1,y2], axis = 1)
T = len(y1)
value = 1000                                          # portfolio value
p = 0.01                                              # probability


##### Listing 5.3/5.4: Univariate HS VaR in MATLAB Last updated 2011

ys = sort(y1);       % sort returns
op = T*p;            % p percent smallest
VaR1 = -ys(op)*value

##### Listing 5.3/5.4: Univariate HS in Python Last updated June 2018

ys = np.sort(y1)           # sort returns
op = int(T*p)              # p percent smallest
VaR1 = -ys[op - 1] * value
print(VaR1)


##### Listing 5.5/5.6: Multivariate HS VaR in MATLAB Last updated 2011

w = [0.3; 0.7];       % vector of portfolio weights
yp = y*w;             % portfolio returns
yps = sort(yp);
VaR2 = -yps(op)*value

##### Listing 5.5/5.6: Multivariate HS in Python Last updated June 2018

w = [[0.3], [0.7]]               # vector of portfolio weights
yp = np.squeeze(np.matmul(y, w)) # portfolio returns
yps = np.sort(yp)
VaR2= -yps[op - 1] * value
print(VaR2)


##### Listing 5.7/5.8: Univariate ES in MATLAB Last updated 2011

ES1 = -mean(ys(1:op))*value

##### Listing 5.7/5.8: Univariate ES in Python Last updated June 2018

ES1 = -np.mean(ys[:op]) * value
print(ES1)


##### Listing 5.9/5.10: Normal VaR in MATLAB Last updated 2011

sigma = std(y1);                   % estimate volatility
VaR3 = -sigma * norminv(p) * value

##### Listing 5.9/5.10: Normal VaR in Python Last updated June 2018

sigma = np.std(y1, ddof=1)                # estimate volatility
VaR3 = -sigma * stats.norm.ppf(p) * value
print(VaR3)


##### Listing 5.11/5.12: Portfolio normal VaR in MATLAB Last updated 2011

sigma = sqrt(w' * cov(y) * w);       % portfolio volatility
VaR4 = - sigma * norminv(p) *  value

##### Listing 5.11/5.12: Portfolio normal VaR in Python Last updated June 2018

## portfolio volatility
sigma = np.sqrt(np.mat(np.transpose(w))*np.mat(np.cov(y,rowvar=False))*np.mat(w))[0,0]
## Note: [0,0] is to pull the first element of the matrix out as a float
VaR4 = -sigma * stats.norm.ppf(p) * value
print(VaR4)


##### Listing 5.13/5.14: Student-t VaR in MATLAB Last updated 2011

scy1=y1*100;                                   % scale the returns
res=mle(scy1,'distribution','tlocationscale');
sigma1 = res(2)/100;                           % rescale the volatility
nu = res(3);
VaR5 = - sigma1 * tinv(p,nu) * value

##### Listing 5.13/5.14: Student-t VaR in Python Last updated June 2018

scy1 = y1 * 100                       # scale the returns
res = stats.t.fit(scy1)
sigma = res[2]/100                    # rescale volatility
nu = res[0]
VaR5 = -sigma*stats.t.ppf(p,nu)*value
print(VaR5)


##### Listing 5.15/5.16: Normal ES in MATLAB Last updated June 2018

sigma = std(y1);
ES2=sigma*normpdf(norminv(p))/p * value

##### Listing 5.15/5.16: Normal ES in Python Last updated June 2018

sigma = np.std(y1, ddof=1)
ES2 = sigma * stats.norm.pdf(stats.norm.ppf(p)) / p * value
print(ES2)


##### Listing 5.17/5.18: Direct integration ES in MATLAB Last updated 2011

VaR = -norminv(p);

##### Listing 5.17/5.18: Direct integration ES in Python Last updated June 2018

VaR = -stats.norm.ppf(p)
integrand = lambda q: q * stats.norm.pdf(q)
ES = -sigma * quad(integrand, -np.inf, -VaR)[0] / p * value
print(ES)


##### Listing 5.19/5.20: MA normal VaR in MATLAB Last updated June 2018

WE=20;
for t=T-5:T
t1=t-WE+1;
window=y1(t1:t);                   % estimation window
sigma=std(window);
VaR6 = -sigma * norminv(p) * value
end

##### Listing 5.19/5.20: MA normal VaR in Python Last updated June 2018

WE = 20
for t in range(T-5,T+1):
t1 = t-WE
window = y1[t1:t]                     # estimation window
sigma = np.std(window, ddof=1)
VaR6 = -sigma*stats.norm.ppf(p)*value
print (VaR6)


##### Listing 5.21/5.22: EWMA VaR in MATLAB Last updated 2011

lambda = 0.94;
s11 = var(y1(1:30));                              % initial variance
for t = 2:T
s11 = lambda * s11  + (1-lambda) * y1(t-1)^2;
end
VaR7 = -norminv(p) * sqrt(s11) * value

##### Listing 5.21/5.22: EWMA VaR in Python Last updated June 2018

lmbda = 0.94
s11 = np.var(y1[0:30], ddof = 1)             # initial variance
for t in range(1, T):
s11 = lmbda*s11 + (1-lmbda)*y1[t-1]**2
VaR7 = -np.sqrt(s11)*stats.norm.ppf(p)*value
print(VaR7)


##### Listing 5.23/5.24: Two-asset EWMA VaR in MATLAB Last updated 2011

s = cov(y);                                              % initial covariance
for t = 2:T
s = lambda * s +  (1-lambda) * y(t-1,:)' * y(t-1,:);
end
sigma = sqrt(w' * s * w);                                % portfolio vol
VaR8 = - sigma * norminv(p) * value

##### Listing 5.23/5.24: Two-asset EWMA VaR in Python Last updated June 2018

## s is the initial covariance
s = np.cov(y, rowvar = False)
for t in range(1,T):
s = lmbda*s+(1-lmbda)*np.transpose(np.asmatrix(y[t-1,:]))*np.asmatrix(y[t-1,:])
sigma = np.sqrt((np.transpose(w)*s*w)[0,0])
## Note: [0,0] is to pull the first element of the matrix out as a float
VaR8 = -sigma * stats.norm.ppf(p) * value
print(VaR8)


##### Listing 5.25/5.26: GARCH in MATLAB Last updated August 2016

[parameters,ll,ht]=tarch(y1,1,0,1);
omega = parameters(1)
alpha = parameters(2)
beta = parameters(3)
sigma2 = omega + alpha*y1(end)^2 + beta*ht(end) % calc sigma2 for t+1
VaR9 = -sqrt(sigma2) * norminv(p) * value

##### Listing 5.25/5.26: GARCH VaR in Python Last updated June 2018

from arch import arch_model
am = arch_model(y1, mean = 'Zero', vol='Garch', p=1, o=0, q=1, dist='Normal')
res = am.fit(update_freq=5)
omega = res.params[0]
alpha = res.params[1]
beta = res.params[2]
## computing sigma2 for t+1
sigma2 = omega + alpha*y1[T-1]**2 + beta * res.conditional_volatility[-1]**2
VaR9 = -np.sqrt(sigma2) * stats.norm.ppf(p) * value
print(VaR9)
## Note: arch_model's GARCH optimization has issues with convergence